Three 100 resistors are connected as shown in the figure. The maximum power that

Question

Three 100 resistors are connected as shown in the figure. The maximum power that can safely be delivered to any one resistor is 26.0 W.

(a) What is the maximum potential difference that can be applied to the terminals a and b?
___V

(b) For the voltage determined in part (a), what is the power delivered to each resistor?

(c) What is the total power delivered to the combination of resistors?
___W

Explanation / Answer

There is a 100 in series with a parallel combination of two 100 resistors.

Solution ---

As per the given condition each resistor can safely bear a power input = 26.0 W.

Hence the maxiumum current allowed through any of the given resistor

( I ) = [ power / Resistance ]

=> I = [ 26.0 / 100 ] = 0.5099 A

Hence considering the assumed circuit the resistance in series can have maximum current = 0.5099 A, while each of the two connected in parallel will have currenet = (1/2) ( 0.5099 ) = 0.2549 A

Again total curcuit resistance = 100 + (100/2) = 150

Hence the maximum permissible voltage = 0.5099 x 150 = 76.48 V

.........................................

Power delivered to the series resistor = (current)^2 x Resistance

=> (0.5099)^2 x 100 = 25.99 approximately = ( 26 ) W.... Answer

Power delivered to each of the resistances in parallel = (0.2549)^2 x 100 = 6.4974 W ........... Answer

Total Power delivered = 26 + (1/2) (26) = 39 Watt .... Answer

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